Death.
No, wait.
Taxes.
The suckitude of my life.
No, wait. That’s my least favorite constant.
[QUOTE=Mbossa]
I’d like to go a step further and pick an undefinable constant. It should be an easy task, since there are “infinitely more” undefinable numbers than definable ones, but oddly enough nobody seems to have defined any.
[/QUOTE]
Pick your favorite well-ordering on R and choose the least undefinable number in [0, 1]. Couldn’t be simpler.
“Cook’s Constant”
The number that when added to, or subtracted from, the answer you got, gives you the answer you should have got. 
I’m going to put in a vote for the fine structure constant, which is discussed here: Fine-structure constant - Wikipedia
That 1/137 just gives me goosebumps!
Favorite is ε[sub]0[/sub], the permittivity of free space. It’s just really useful.
I absolutely hate Planck’s (and Dirac’s) constant. They remind me of extremely bad times in my life.
Another vote for pi. Picturing a polygon (with its perimeter and the altitude of one of its sides drawn in a thick dark line) with an ever increasing number of sides eventually morphing into a perfect circle, well, it makes my heart go all fluttery and my eyes get that far-away dreamy look.
“John Constantine: Hellblazer.”
My favorite is the Hubble constant, because it can’t yet be measured accurately, and may not actually be constant. Premature nomenclatural assumptions tickle me in that special place. 
Twenty-nine posts and no one’s mentioned my choice, the speed of light in vacuum? I don’t know whether to be pleased or shocked.
c = 3.00 x 10^8 m/s, so beautiful and easy to make estimations with.
i = (-1)^(1/2)
In eleventh grade pre-calc, our first assignment of the year was to write about our feelings on math. I wrote a fairie tale based around imaginary numbers. They bring me great joy.
[QUOTE=Nametag]
I’m going to put in a vote for the fine structure constant, which is discussed here: Fine-structure constant - Wikipedia
That 1/137 just gives me goosebumps!
[/QUOTE]
That is my favorite, but it really isn’t 1/137 any more than pi is 22/7.
[QUOTE=MissMossie]
i = (-1)^(1/2)
In eleventh grade pre-calc, our first assignment of the year was to write about our feelings on math. I wrote a fairie tale based around imaginary numbers. They bring me great joy.
[/QUOTE]
I like *i * a whole lot too, and especially -i ::brain explodes
It looks lemon yellow with a hint of lime in my mind.